Functional magnetic resonance imaging (fMRI) is used to extract functional networks connecting correlated human brain sites. Analysis of these networks shows that the distribution of functional connections and the probability of finding a link vs. distance are both scale-free. The characteristic path length is small and comparable to those of equivalent random networks, while the clustering coefficient is orders of magnitude larger than those of equivalent random networks. These properties, typical of scale-free small-world networks, reflect important functional information about brain states. The study uses fMRI to extract functional networks and analyzes them in the context of complex network theory. The method involves calculating the linear correlation coefficient between pairs of voxels to determine functional connections. The degree distribution of the networks shows a power law decay, indicating a scale-free structure. The results are robust across different subjects and task conditions, showing consistent power law scaling in the degree distribution and link probability. The networks exhibit small-world properties, with short path lengths and high clustering coefficients. The study also finds that the networks are assortative, with highly connected nodes tending to connect to other well-connected nodes. These properties are consistent across different brain states, such as listening to music and finger tapping. The results show that the human brain network has small-world properties and scale-free characteristics, which are robust across parameters, subjects, and task conditions. These findings suggest that the brain's functional networks have invariant properties, and they provide a novel perspective on the dynamics of brain states, particularly in cases of dysfunction. The study also highlights the importance of further research into the origins of these scaling laws and their implications for understanding brain function and pathology.Functional magnetic resonance imaging (fMRI) is used to extract functional networks connecting correlated human brain sites. Analysis of these networks shows that the distribution of functional connections and the probability of finding a link vs. distance are both scale-free. The characteristic path length is small and comparable to those of equivalent random networks, while the clustering coefficient is orders of magnitude larger than those of equivalent random networks. These properties, typical of scale-free small-world networks, reflect important functional information about brain states. The study uses fMRI to extract functional networks and analyzes them in the context of complex network theory. The method involves calculating the linear correlation coefficient between pairs of voxels to determine functional connections. The degree distribution of the networks shows a power law decay, indicating a scale-free structure. The results are robust across different subjects and task conditions, showing consistent power law scaling in the degree distribution and link probability. The networks exhibit small-world properties, with short path lengths and high clustering coefficients. The study also finds that the networks are assortative, with highly connected nodes tending to connect to other well-connected nodes. These properties are consistent across different brain states, such as listening to music and finger tapping. The results show that the human brain network has small-world properties and scale-free characteristics, which are robust across parameters, subjects, and task conditions. These findings suggest that the brain's functional networks have invariant properties, and they provide a novel perspective on the dynamics of brain states, particularly in cases of dysfunction. The study also highlights the importance of further research into the origins of these scaling laws and their implications for understanding brain function and pathology.